People who don’t believe in absolute moral standards also tend to believe that no one should impose their personal moral standards on others.
Think about people you’ve known - either personally, in the news, or from history - who did something horrifically wrong. For you to know their actions were wrong, you must have an idea of what is right. This means you have an awareness of a moral “standard.” Because you believe the behavior is wrong for that person or group, it can be presumed that you believe it’s wrong for all people and groups. That would make your moral standard absolute. It applies to everyone.